12 research outputs found
On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
In this paper we study the nonperturbative corrections to the generalized
Konishi anomaly that come from the strong coupling dynamics of the gauge
theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge
theory with symmetric or antisymmetric tensor. We study the algebra of chiral
rotations of the matter field and show that it does not receive nonperturbative
corrections. The algebra implies Wess-Zumino consistency conditions for the
generalized Konishi anomaly which are used to show that the anomaly does not
receive nonperturbative corrections for superpotentials of degree less than
2l+1 where 2l=3c(Adj)-c(R) is the one-loop beta function coefficient. The
superpotentials of higher degree can be nonperturbatively renormalized because
of the ambiguities in the UV completion of the gauge theory. We discuss the
implications for the Dijkgraaf-Vafa conjecture.Comment: 23 page
Low Energy Effective Action in N=2 Yang-Mills as an Integrated Anomaly
Based on chiral ring relations and anomalies, as described by Cachazo,
Douglas, Seiberg and Witten, we argue that the holomorphic effective action in
N=2 Yang-Mills theory can be understood as an integrated U(1) anomaly from a
purely field theory point of view. In particular, we show that the periods of
the Riemann surface arising from the generalized Konishi anomaly can be given a
physical interpretation without referring to special geometry. We also discuss
consequences for the multi-instanton calculus in N=2 Yang-Mills theory.Comment: 25 pages, 2 figures ; v2: reference adde
Generalized Konishi anomaly, Seiberg duality and singular effective superpotentials
Using the generalized Konishi anomaly (GKA) equations, we derive the
effective superpotential of four-dimensional N=1 supersymmetric SU(n) gauge
theory with n+2 fundamental flavors. We find, however, that the GKA equations
are only integrable in the Seiberg dual description of the theory, but not in
the direct description of the theory. The failure of integrability in the
direct, strongly coupled, description suggests the existence of
non-perturbative corrections to the GKA equations.Comment: 20 pages; v3: corrected the comparison to the SU(2) cas
Sp(N) higher-derivative F-terms via singular superpotentials
We generalize the higher-derivative F-terms introduced by Beasley and Witten
(hep-th/0409149) for SU(2) superQCD to Sp(N) gauge theories with fundamental
matter. We generate these terms by integrating out massive modes at tree level
from an effective superpotential on the chiral ring of the microscopic theory.
Though this superpotential is singular, its singularities are mild enough to
permit the unambiguous identification of its minima, and gives sensible answers
upon integrating out massive modes near any given minimum.Comment: 15 pages, 6 figure
On singular effective superpotentials in supersymmetric gauge theories
We study N=1 supersymmetric SU(2) gauge theory in four dimensions with a
large number of massless quarks. We argue that effective superpotentials as a
function of local gauge-invariant chiral fields should exist for these
theories. We show that although the superpotentials are singular, they
nevertheless correctly describe the moduli space of vacua, are consistent under
RG flow to fewer flavors upon turning on masses, and also reproduce by a
tree-level calculation the higher-derivative F-terms calculated by Beasely and
Witten (hep-th/0409149) using instanton methods. We note that this phenomenon
can also occur in supersymmetric gauge theories in various dimensions.Comment: 21 pages, 5 figures; minor errors correcte
Effective action for Einstein-Maxwell theory at order RF**4
We use a recently derived integral representation of the one-loop effective
action in Einstein-Maxwell theory for an explicit calculation of the part of
the effective action containing the information on the low energy limit of the
five-point amplitudes involving one graviton, four photons and either a scalar
or spinor loop. All available identities are used to get the result into a
relatively compact form.Comment: 13 pages, no figure
Effective superpotential for U(N) with antisymmetric matter
We consider an N=1 U(N) gauge theory with matter in the antisymmetric
representation and its conjugate, with a tree level superpotential containing
at least quartic interactions for these fields. We obtain the effective
glueball superpotential in the classically unbroken case, and show that it has
a non-trivial N-dependence which does not factorize. We also recover additional
contributions starting at order S^N from the dynamics of Sp(0) factors. This
can also be understood by a precise map of this theory to an Sp(2N-2) gauge
theory with antisymmetric matter.Comment: 22 pages. v2: comment (and a reference) added at the end of section 2
on low rank cases; minor typos corrected. v3: 2 footnotes added with
additional clarifications; version to appear in journa
Glueball operators and the microscopic approach to N=1 gauge theories
We explain how to generalize Nekrasov's microscopic approach to N=2 gauge
theories to the N=1 case, focusing on the typical example of the U(N) theory
with one adjoint chiral multiplet X and an arbitrary polynomial tree-level
superpotential Tr W(X). We provide a detailed analysis of the generalized
glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa
matrix model and of the generalized Konishi anomaly equations. We compute in
particular the non-trivial quantum corrections to the Virasoro operators and
algebra that generate these equations. We have performed explicit calculations
up to two instantons, that involve the next-to-leading order corrections in
Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of
references corrected, version to appear in JHE
Tree-Level Formalism
We review two novel techniques used to calculate tree-level scattering
amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the
MHV diagrams, we consider applications to tree-level amplitudes and focus in
particular on the N=4 supersymmetric formulation. We also briefly describe the
derivation of loop amplitudes using MHV diagrams. For the recursion relations,
after presenting their general proof, we discuss several applications to
massless theories with and without supersymmetry, to theories with massive
particles, and to graviton amplitudes in General Relativity. This article is an
invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of
Physics A devoted to "Scattering Amplitudes in Gauge Theories", R.
Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections,
references adde
Hidden Simplicity of Gauge Theory Amplitudes
These notes were given as lectures at the CERN Winter School on Supergravity,
Strings and Gauge Theory 2010. We describe the structure of scattering
amplitudes in gauge theories, focussing on the maximally supersymmetric theory
to highlight the hidden symmetries which appear. Using the BCFW recursion
relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,
and describe how it produces a sum of invariants of a large symmetry algebra.
We review amplitudes in the planar theory beyond tree-level, describing the
connection between amplitudes and Wilson loops, and discuss the implications of
the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe